Cohen's d (Effect Size) Calculator
Standardized difference between two means.
Formula first
Overview
Cohen's d is a standardized measure used to quantify the magnitude of the difference between two group means. It expresses the distance between means in units of standard deviation, allowing researchers to determine the practical significance of a result beyond mere statistical probability.
Symbols
Variables
d = Cohen's d, M_1 = Mean 1, M_2 = Mean 2, SD = Pooled SD
Apply it well
When To Use
When to use: Use Cohen's d when comparing the means of two distinct groups, such as a treatment and control group in an experimental design. It is appropriate when the data is continuous and satisfies the assumptions of normality and homogeneity of variance.
Why it matters: This metric allows psychologists to assess the real-world impact of an intervention regardless of the scale used for measurement. It facilitates meta-analysis by providing a universal metric to compare results across multiple independent studies.
Avoid these traps
Common Mistakes
- Dividing by the wrong SD.
- Ignoring the direction of the effect.
One free problem
Practice Problem
A psychologist tests a new memory enhancement technique. The treatment group has a mean score of 82, while the control group has a mean score of 74. If the pooled standard deviation is 10, what is the Cohen's d effect size?
Solve for:
Hint: Subtract the control mean from the treatment mean, then divide by the standard deviation.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Cohen's d
- Discovering Statistics Using IBM SPSS Statistics (Andy Field)
- Wikipedia: Effect size
- Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth Cengage Learning.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.
- Field, A. (2018). Discovering Statistics Using R (5th ed.). SAGE Publications.
- University Psychology — Statistics